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%I #21 Oct 02 2018 12:54:42
%S 1,1,2,4,7,13,25,46,86,161,300,560,1046,1952,3644,6803,12699,23706,
%T 44254,82611,154215,287883,537408,1003212,1872757,3495988,6526172,
%U 12182800,22742368,42454552,79252477,147945385,276178586,515559248
%N Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=1, r=5, I={3,4}.
%C Number of compositions (ordered partitions) of n into elements of the set {1,2,3,6}.
%C Number of compositions of n with 3 frozen; that is, the order of the summand 3 does not matter. - _Gregory L. Simay_, Oct 01 2018
%D D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970.
%H Vladimir Baltic, <a href="http://pefmath.etf.rs/vol4num1/AADM-Vol4-No1-119-135.pdf">On the number of certain types of strongly restricted permutations</a>, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (2010), 119-135
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,0,0,1).
%F a(n) = a(n-1)+a(n-2)+a(n-3)+a(n-6).
%F G.f.: -1/(x^6+x^3+x^2+x-1)
%o (PARI) x='x+O('x^50); Vec(1/(1-x-x^2-x^3-x^6)) \\ _Altug Alkan_, Oct 02 2018
%Y Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.
%K nonn
%O 0,3
%A _Vladimir Baltic_, Feb 19 2003
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